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Nonlinear rigid block dynamics


Pich, Peter (1995) Nonlinear rigid block dynamics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2gsn-6v23.


Motion of a block on flat ground under the influence of gravity is studied.

A general model is introduced for the free motion of a rectangular, rigid block on a continuous, perfectly elastic foundation. The model includes friction forces between the block and foundation and allows for sliding, rocking and flight of the block. Solutions are obtained through numerical integration. A three parameter study is carried out, namely as a function of aspect ratio, r, coefficient of friction, µ and non-dimensional stiffness, k_, for various initial conditions.

Dominant types of response are identified and the stability of the block against overturning and its tendency to fly are studied. For initial conditions with sufficient energy, critical curves are found in the (k_, r) parameter space which define a transition between a flight and no flight region. For initial conditions with sufficient energy there also exists a critical curve in the same parameter space which separates a region of overturning from a region where the block does not overturn.

Chaos is found in the flight region of the (k_,r) parameter space for sufficiently high r. Poincare maps and Liapunov exponents are computed to document the existence of chaos.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied Mechanics
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Hall, John F.
Thesis Committee:
  • Unknown, Unknown
Defense Date:12 December 1994
Record Number:CaltechTHESIS:12012011-112223883
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6746
Deposited By: Benjamin Perez
Deposited On:05 Dec 2011 16:19
Last Modified:09 Nov 2022 19:19

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